Abstract
We construct a new family of entire solutions for the nonlinear Schrödinger equation{−Δu+V(y)u=up,u>0,inRN,u∈H1(RN), where p∈(1,N+2N−2) and N≥3, and V(y)=V(|y|) is a positive bounded radial potential satisfyingV(|y|)=V0+a|y|m+O(1|y|m+σ),as|y|→∞, for some fixed constants V0,a,σ>0, and m>max{4p−1,2}.
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